1358
Inorg. Chem. 2001, 40, 1358-1362
Iron Pentacarbonyl: Are the Axial or the Equatorial Iron-Carbon Bonds Longer in the Gaseous Molecule? Bruce W. McClelland,† Alan G. Robiette,† Lise Hedberg, and Kenneth Hedberg* Department of Chemistry, Oregon State University, Corvallis, Oregon 97331 ReceiVed October 10, 2000
The structure of iron pentacarbonyl, Fe(CO)5, was reinvestigated by gas-phase electron diffraction using an experimental rotational constant available from the literature as a constraint on the structural parameters. The study utilized a B3LYP/6-311+G(d) ab initio quadratic force field, scaled to fit observed infrared wavenumbers, from which were calculated corrections for the effects of vibrational averaging on distances and certain other quantities useful for the structural analysis. The results confirm that the equatorial Fe-C bonds are longer than the axial ones, an important difference with the structure in the crystal where the equatorial Fe-C bonds are the shorter. Some distance (rg/Å) and vibrational amplitude (lR/Å) parameter values with estimated 2σ uncertainties based on assumption of D3h symmetry are 〈r(Fe-C)〉 ) 1.829(2), r(Fe-C)eq - r(Fe-C)ax ) 0.032(20), 〈r(CdO)〉 ) 1.146(2), r(CdO)eq - r(CdO)ax ) 0.006(27), r(Fe-C)ax ) 1.810(16), r(Fe-C)eq ) 1.842(11), r(CdO)ax ) 1.142(23), r(CdO)eq ) 1.149(16), l(Fe-C)ax ) l(Fe-C)eq ) 0.047(5), and l(CdO)ax ) l(CdO)eq ) 0.036(3).
Introduction The molecular structure of iron pentacarbonyl, Fe(CO)5, hereafter IPC, has been thoroughly studied by experimental and theoretical methods that span more than three decades. Among the former are several gas-phase electron-diffraction investigations,1-4 an X-ray diffraction study of the crystal,5 IR and Raman studies,6,7 and an FTIR study of the rovibrational spectrum.8 The theoretical (ab initio) work includes calculations at the HF,9,10 DFT,10-14 MP,10 and CI11 levels with various bases. Results from both the experimental and theoretical side agree that the molecule has a trigonal bipyramidal structure (D3h symmetry), but there is considerable uncertainty about the relative lengths of the axial and equatorial Fe-C bonds. It was concluded from the electron-diffraction (GED) studies that the axial Fe-C bond is the shorter by a small amount [0.049 ( 020 Å,1 0.027 (σ ) 0.005) Å,2 0.000-0.050 Å,3 and 0.020 ( † Present addresses: B.W.M., Central Oregon Community College, 2600 College Way, Bend, OR 97701; A.G.R, 30 High Street, Warwick CV34 3AX, United Kingdom. (1) Davis, M. I.; Hanson, H. P. J. Phys. Chem. 1965, 69, 3405. Davis, M. I.; Hanson, H. P. J. Phys. Chem. 1967, 71, 775. (2) Beagley, B.; Cruickshank, D. W. J.; Pinder, P. M.; Robiette, A. G.; Sheldrick, G. M. Acta Crystallog., Sect. B 1969, 25, 737. (3) Almenningen, A.; Haaland, A.; Wahl, K. Acta Chem. Scand. 1969, 23, 2245. (4) Beagley, B.; Schmidling, D. G. J. Mol. Struct. 1974, 22, 466. (5) Braga, D.; Grepion, F.; Orpen, A. G. Organometallics 1993, 12, 1481. (6) Jones, L. H.; McDowell, R. S.; Goldblatt, M.; Swanson, B. I. J. Chem. Phys. 1972, 57, 2050. (7) Matsumoto, Y.; Majima, T.; Takami, M. Mol. Phys. 1987, 61, 1045. (8) Asselin, P.; Soulard, P.; Tarrago, G.; Lacome, N.; Manceron, L. J. Chem. Phys. 1996, 104, 4427. (9) Lu¨thi, H. P.; Siegbahn, P. E. M.; Almlo¨f, J. J. Phys. Chem. 1985, 89, 2156. (10) Jonas, V.; Thiel, W. J. Chem. Phys. 1995, 102, 8474. (11) Be´rces, A.; Ziegler, T. J. Phys. Chem. 1995, 99, 11417. (12) Li, J.; Schreckenback, G.; Ziegler, T. J. Am. Chem. Soc. 1995, 117, 486. (13) Jang, J. H.; Lee, J. G.; Lee, H.; Xie, Y.; Schaefer, H. F., III. J. Phys. Chem. A 1998, 102, 5298. (14) Gonza´lez-Blanco, O.; Branchadell, V. J. Chem. Phys. 1999, 110, 778.
0.006 Å4]. In the crystal, however, the axial Fe-C bond is found to be longer by 0.007-0.010 Å.5 The theoretical results are also divided on this matter: most of those from higher level calculations predict a slightly longer axial bond, but the difference is usually only a few thousandths of an angstrom. Some 25 years ago-before the most recent of the GED studies4stwo of us (A.G.R. and K.H.) also undertook a GED study of IPC at this university. As in the other studies, a good fit to our diffraction data was easily obtained with the axial Fe-C bonds slightly shorter than the equatorial ones, but with some creative variation of the corrections for vibrational averaging (“shrinkage”15) and the relative lengths of the two types of CdO bonds, a fit of similar quality could also be obtained with axial Fe-C bonds longer than the equatorial. This work was never published, but it was concluded that the question of the relative Fe-C bond lengths could probably not be reliably answered from GED data alone. After the GED work mentioned above, the two cited reports7,8 of high-resolution IR work on freely expanding jets of IPC have yielded a value for B0. This quantity together with our GED data gave hope for a definitive answer to the question, and accordingly we decided to attack the problem again. This article is an account of our results. Experimental Section Although our old data were thought to be satisfactory for this reinvestigation, there have been many improvements in the Oregon State University GED experiment and data analysis procedures. We thus decided to prepare new diffraction photographs, which would be handled by our current procedures, and also to reanalyze the older photographs with the new procedures. An important consequence of this approach was a check on the scale of the molecule. The accuracy of the scale, or size, of the molecule depends on the accuracy of the wavelength and camera-distance measurements, which have been much improved since the old data were gathered. Obviously, an accurate molecular size is vitally important if rotational constants are to be used as auxiliary data in the GED analysis of the structure. (15) Bastiansen, O.; Trætteberg, M. Acta Crystallogr. 1960, 13, 1108.
10.1021/ic001114e CCC: $20.00 © 2001 American Chemical Society Published on Web 02/10/2001
Fe-C Bonds in Iron Pentacarbonyl
Inorganic Chemistry, Vol. 40, No. 6, 2001 1359
Table 1. Experimental Conditions for Electron-Diffraction Experiments old dataa camera dist/mm electron wavelength/Å exposure time/s beam current/µA bulk sample temp/K no. of plates/films used data range, s/Å-1 data interval, ∆s/Å-1 a
new dataa
LC
MC
SC
LC
MC
750.0 0.058 45-105 0.39-0.40 273 5 1.0-14.0 0.25
300.1 0.058 60-165 0.36-0.41 273 5 7.5-33.75 0.25
120.6 0.058 240-360 0.45-0.47 287 3 22.75-60.0 0.25
746.8 0.050 75-105 0.54-0.56 264 3 2.0-16.25 0.25
299.7 0.050 120-150 0.53-0.55 271 2 7.5-38.5 0.25
Definitions: LC, long camera; MC, middle camera; SC, short camera.
Figure 2. Radial distribution curves. The experimental curve is calculated from the average intensity curves with theoretical data for the unobserved range s e 1.75 Å-1 and a convergence factor B ) 0.0020 Å2. Vertical bars indicate the interatomic distances in model A; the lengths of the bars are proportional to the weights of the terms. The difference curve is experimental minus theoretical for model A. electron-scattering amplitude. These scattering amplitudes and their corresponding phases used in other calculations were obtained from tables.18
Theoretical Calculations
Figure 1. Intensity curves. Long and middle camera curves are magnified five times relative to their backgrounds on which they are superimposed. Average curves are in the form sIm(s). The theoretical curve is calculated from model A of Table 2 and includes the multiple scattering component. Difference curves are experimental minus theoretical. Commercially prepared IPC (Ventron, purity >99.5%, for the older experiments and Aldrich Chemical Co., 99.999% pure, for the newer experiments) were used without further purification in the Oregon State University apparatus, in all cases with a nozzle-tip temperature of 295296 K. Other experimental conditions are summarized in Table 1. Procedures for obtaining the total scattered electron-intensity distribution, s4It(s), and for removing the backgrounds to yield molecular intensities in the form sIm(s) are familiar.16,17 The intensity curves from the newer data are shown in Figure 1; those from the older data are similar. The experimental intensity data are available as Supporting Information. Radial distribution curves, such as that shown in Figure 2, were calculated by Fourier transformation of the function sIm(s)ZFeZC(s4FFeFC)-1 exp(-0.002s2), where F is the absolute value of the complex (16) Gundersen, G.; Hedberg, K. J. Chem. Phys. 1969, 51, 2500. (17) Hedberg, L. Abstracts of Papers, Fifth Austin Symposium on GasPhase Molecular Structure, Austin, TX, Mar 1974; University of Texas: Austin, TX, 1974; p 37.
The plan to incorporate B0 as an observable, or constraint, in the structure refinement of IPC required both ab initio and normal coordinate calculations. The ab initio calculations establish likely differences between the CdO bond lengths should they be needed in the course of the refinements, and provide a Cartesian quadratic force field for use in the normal coordinate work. The normal coordinate calculations provide the array of corrections to distances and to B0, which are required for consistency between the measurements of GED (distance space ra) and spectroscopy (B0),19 and estimates of vibrational amplitudes that would be difficult to measure experimentally. Although the variety of ab initio calculations cited above9-14 offer some of these data, it was convenient to carry out our own calculations making use of a level of theory and a basis set in which we have developed some confidence for the purposes intended here. We selected a B3LYP/6-311+G(d) (18) Elastic amplitudes and phases: Ross, A. W.; Fink, M.; Hilderbrandt, R. L. International Tables for Crystallography; Kluwer: Boston, Dordrecht, London, 1992; Vol. 4, p 245. Inelastic amplitudes: Cromer, D. T.; Mann, J. B. J. Chem. Phys. 1967, 47, 1892. Cromer, D. T. J. Chem. Phys. 1969, 50, 4857. (19) For a summary of the relationship between the methods of rotational spectroscopy and electron diffraction, see: Robiette, A. G. In Molecular Structure by Diffraction Methods; Specialist Periodical Reports; The Chemical Society: London, 1973; Vol. 1.
1360 Inorganic Chemistry, Vol. 40, No. 6, 2001
McClelland et al.
Table 2. Parameter Values for Iron Pentacarbonyla this work model 〈r(Fe-C)〉 r(Fe-C)eq - r(Fe-C)ax 〈r(CdO)〉 r(CdO)eq - r(CdO)ax Bz(exp) - Bz(theor)i Rj
Ac
1.829(2) 0.032(20) 1.146(2) 0.006(27) 0.17 0.066
model B
d
1.826(2) 0.016(19) 1.146(2) 0.004(26) 0.11 0.065
model Ce
model Df
model Eg
GED3
GED4
XRD5
theoretb
1.829(2) 0.021(21) 1.146(2) -0.001(28) 2.04 0.065
1.826(2) 0.014(20) 1.146(2) 0.002(27) 0.30 0.065
1.815(2) 0.021(22) 1.139(1) -0.002(33) -9.70 0.095
1.827(3) 0.012(6) 1.147(2) 0.0h
1.821(6) 0.020(12) 1.153(6) 0.0h
1.806 -0.007, -0.010 1.127 -0.011, 0.019
1.824 -0.007 1.141 0.004
a Distances are rg/Å, and rotational constant difference in MHz. Quantities in parentheses are estimated uncertainties: 2σ including possible systematic error for all GED work and, apparently, σ for ref 5. b B3LYP/6-311+G(d). c New GED data, Bz value and multiple scattering included. d New GED data, B value only included. e New GED data, B value ignored, effects of multiple scattering included. f New GED data only. g Old z z GED data only. h Assumed. i B0 ) 804.220 MHz; Bz ) 804.060 MHz. j Goodness of fit factor. R ) [∑iwi∆i2/∑i(siIi(obsd))2]1/2, where ∆i ) siIi(obsd) - siIi(calcd).
calculation, which was carried out with the program G98W.20 The Cartesian force field from the ab initio calculation was symmetrized and modified by program ASYM4021 to fit the observed vibrational wavenumbers6 as partially reassigned by others.10-12 The distance conversion factors, ra f rR0 ) rz, obtained from the modified force field may be deduced from the table of final results; the rotational-constant conversion from this force field was B0 - 0.16 ) Bz(rz). Structure Refinements The structure of IPC was refined by least squares21 using both the older and newer data. The molecule was assumed to have D3h symmetry which required four distance parameters to describe its geometry. These were chosen to be the average Fe-C bond length, 〈r(Fe-C)〉 ) [2r(Fe-C)ax + 3r(Fe-C)eq]/ 5, the difference between the two types of iron-carbon distances, ∆r(Fe-C) ) r(Fe-C)eq - r(Fe-C)ax, and similar definitions for the parameters involving the CdO bonds. A number of the vibrational amplitude parameters-in principle one for each different distance term-were expected to be nearly equal and were confirmed to be so by the theoretical calculations. These amplitudes were either set equal to each other or given a set difference and then refined in pairs. In all, 10 amplitude parameters were refined. Refinements were carried out under a variety of conditions. Some were based only on the GED data (old and new separately), and others included the rotational constant as an additional observable. It proved impossible to obtain a precise value for the parameter ∆r(CdO) under unrestrained conditions, which led us to introduce a “predicate”22 value for it equal to 0.0037 (σ ) 0.0018) Å. This value is the average of those obtained from the ab initio calculations9-14 including our own. The standard deviation served as an initial guess for the predicate weighting. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (21) Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 2000, 203, 82. For an earlier version of this program that did not permit the input and symmetrization of Cartesian force constants, see: Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 1993, 160, 117.
Table 3. Distances (r/Å) and Vibrational Amplitudes (l/Å) for Preferred Model A of Iron Pentacarbonyl param
rR0
rg
ra
lexp
ltheor
(Fe-C)ax (Fe-C)eq (CdO)ax (CdO)eq (Fe‚‚‚O)ax (Fe‚‚‚O)eq Cax‚‚‚Ceq Ceq‚‚‚Ceq Cax‚‚‚Oeq Ceq‚‚‚Oax Ceq‚‚‚Oeq Oax‚‚‚Oeq Oeq‚‚‚Oeq Cax‚‚‚Cax Cax‚‚‚Oax Oax‚‚‚Oax
1.806(16) 1.837(11) 1.136(23) 1.141(16) 2.941(9) 2.979(7) 2.576(5) 3.182(20) 3.483(13) 3.468(13) 4.210(9) 4.186(5) 5.159(13) 3.611(33) 4.747(13) 5.883(19)
1.810 1.842 1.142 1.149 2.945 2.983 2.580 3.185 3.487 3.472 4.213 4.191 5.162 3.614 4.750 5.885
1.809 1.841 1.141 1.148 2.944 2.982 2.574 3.180 3.479 3.464 4.205 4.177 5.147 3.612 4.748 5.884
0.047 (5) 0.047 0.036 (3) 0.036 0.048 (4) 0.048 0.118(14) 0.130(58) 0.172 (21) 0.172 0.179 (25) 0.240 0.280(200) 0.071 (23) 0.071 0.073(49)
0.051 0.051 0.035 0.035 0.051 0.051 0.122 0.144 0.166 0.167 0.186 0.247 0.260 0.064 0.064 0.065
} } } } } }
The refinements based only on the old and new GED data led to similar results that the equatorial Fe-C bonds were slightly longer than the axial ones. However, a disturbing feature of these refinements was an apparent inconsistency in molecular size wherein the older data suggested a smaller molecule by about 0.6%. Introduction of the rotational constant as a constraint changed the picture obtained from the older data in two ways. First, it was found that both r(Fe-C)ax and r(CdO)ax became much longer than their equatorial counterparts, and second, the vibrational amplitude l(CdO) decreased from a value pleasingly close to the theoretical one to a value fully 30% smaller. Accompanying these changes was a decrease in quality of fit between the observed and calculated intensity distributions of more than 5% as measured by the quality-of-fit parameter R. No such changes occurred when the rotational constant constraint was introduced in the refinements based on our newer GED data; in this case the molecular size was essentially unchanged. With this strong evidence of a scale problem with the older data, we decided that further work would be done only with the newer data. The effects of multiple (three-atom) scattering23 were also tested. We calculated the ITP0 approximate multiple scattering intensity and included it as a contribution to the overall theoretical intensities that resulted from refinements of the (22) Bartell, L. S.; Romenesko, D. J.; Wong, T. C. In Molecular Structure by Diffraction Methods; Specialist Periodical Reports; The Chemical Society: London, 1975; Vol. 3, Chapter 4. The method of predicate values presumes a likely value for the parameter in question, which is allowed to change during the refinement procedure in accordance with one’s confidence in the chosen value expressed as a weight. In effect the refined value is connected to the predicate value with a flexible tether, the strength of which is determined by the weighting. (23) Miller, B. R.; Bartell, L. S. J. Chem. Phys. 1980, 72, 800.
Fe-C Bonds in Iron Pentacarbonyl
Inorganic Chemistry, Vol. 40, No. 6, 2001 1361
Table 4. Correlation Matrix (×100) for Parameters of Model A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 a
param
100σLSa
〈r(Fe-C)〉 ∆r(Fe-C)b 〈r(CdO)〉 ∆r(CdO)b l(Fe-C) l(CdO) l(Fe‚‚‚O) l(Cax‚‚‚Ceq) l(Ceq‚‚‚Ceq) l(Cax‚‚‚Oeq) l(Ceq‚‚‚Oeq) l(Oeq‚‚‚Oeq) l(Cax‚‚‚Cax) l(Oax‚‚‚Oax) r(Fe-C)ax r(Fe-C)eq r(CdO)ax r(CdO)eq
0.04 0.98 0.04 1.37 0.18 0.08 0.13 0.48 2.05 0.72 0.82 7.07 0.81 1.75 0.58 0.40 0.83 0.55
r1
r2
r3
r4
100 19 100 -39 5 100 -2 -95 1 100 -16 -94 -6 90 7 69 -6 -72 -23 52 -10 -71 8
